Questions tagged [quantum-chemistry]
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1answer
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$sp^3$ Hybridization wavefunctions and probability density
I have plotted a hydrogen-like sp3-hybrid orbital probability density and it looks like this:
I can plot 4 overlapping probability densities in a tetrahedral shape:
So far it looks OK.
But when I'm ...
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5answers
80 views
Harnessing molecule vibration energy
Disclaimer: I am learning physics for fun, please dont kill me but explain where I am wrong.
As I understand all molecules have a lowest energy state in which they posses some amount of momentum even ...
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1answer
34 views
1D Infinite Square Well: Box Suddenly Increase in Size. Why the coefficients can be derived by inner producting the wave functions?
I have read the question 1D Infinite Square Well: Box Suddenly Increase in Size. How treat this?. There are two key equations in the selected answer.
$$\int_0^{2L} dx \ \psi^*_m\left(x\right) \Psi\...
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1answer
19 views
Basis Functions for Hartree Fock, and Configuration Interaction
I'm about halfway through the book Szabo and Ostlund, and while I think I understand the rough idea of Hartree-Fock and configuration interaction, there is something I would like to clarify.
For one, ...
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0answers
18 views
Program for calculating transition amplitudes
I calculated transition amplitudes with MBPT analytically and used Slater-Condon rules. Now I have a very long expression and I would like to solve my matrix elements. Does someone know a program for ...
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0answers
21 views
Operator for change of state?
I am trying to model a quantum system that has only three different classical states, so that the Hilbert space is simply $\mathbb C^3$, and let's call its standard basis $e_1,e_2,e_3$, with each of ...
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0answers
47 views
Direction of the permanent dipole moment of the NH$_3$ molecule
What is the direction of dipole moment in a molecule of $\rm NH_3$? Is from hydrogen to nitrogen? Also do we take into account the dipole moment of the lone pair with hydrogen? When we must take into ...
2
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1answer
36 views
How to propagate Heller's model of the Gaussian Wave Packet? [closed]
I'm working on an undergraduate research project on gaussian wave packets, but am a pretty big noob in terms of theoretical chemistry and the like. I'm having a lot of difficulty grasping this concept ...
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0answers
16 views
Bond Type in Orthophosphate
How can we find out the bond nature in LiBaPO4 by using charge transfer values obtained through DFT calculations?
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3answers
169 views
Would an $H_2O$ Molecule actually look like this 3D representation if we could see it?
I'm trying to get a much better grasp on atoms and molecules and I am a visual learner. I found the above image here. This intuitively makes sense to me because I can see how the electron orbitals ...
2
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2answers
37 views
Sign of exchange integral in quantum chemistry?
I have a question about exchange integral in quantum chemistry.
Usually, we learn that the sign of exchange integral is positive, so a triplet state has lower energy than singlet state.
Is it ...
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2answers
56 views
What is the energy of an atomic orbital?
When we refer to energy of an atomic orbital what is this energy ? is potential energy ? but if is potential energy then shouldn't be considered the whole potential energy of the atom ( potential ...
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1answer
105 views
Putting high symmetry points labels to a band structure plot [closed]
So far I've got this plot using Quantum Espresso. I want to put gamma, X, L, etc labels to the k-path.
Quantum Espresso's ouput states the following:
...
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1answer
54 views
What are some molecular systems which have quantum states that are measurably incompatible?
What I'm looking for is a molecular system, which we can produce in a lab, that is,
A discrete variable system (ie, a finite dimensional hilbert space)
It has observables that are incompatible with ...
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1answer
36 views
Electronic configuration
In chemistry the lithium electronic configuration is
$$1s^22s^1 \, .$$
Can we prove this using approximation method like perturbation theory that this the ground state and not for example $1s^22p^...
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0answers
34 views
How to determine symmetry of the system from the term symbol?
I'm studying term symbols. I can derive them mechanically from the electron configuration using the complete table of microstates.
Let's consider a typical example - an atomic carbon with the ...
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0answers
23 views
In what cases (precisely) are Hund's rules valid?
I can't find on any good source (such as a textbook) a precise specification about the cases when Hund's rules (especially Hund's third rule) for an electronic configuration of atom are valid (the ...
2
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1answer
41 views
Planck blackbody radiation
I am reading a chapter about blackbody radiation in my physics textbook, and I encountered the following equation:
$$d\rho(\nu, T)=\rho_\nu(T)d\nu=\frac{8\pi k_BT}{c^3}\nu^2d\nu$$
which is a classical ...
1
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1answer
42 views
Reference request for symmetry breaking Hartree-Fock
Stationary mean-field solutions break symmetries of the many-body Hamiltonian in favour of lowering the energy, e.g. translational or rotational symmetry, despite $[H,P]=0$, or $[H,L_z]=0$, ...
4
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1answer
87 views
What would measuring the position of an electron in an electronic superposition look like?
In view of the Copenhagen interpretation, the state:
$$\Psi = \frac{1}{\sqrt{2}}|0⟩ + \frac{1}{\sqrt{2}}|1⟩$$
is interpreted as "when the system is measured, you have a 50% chance of finding the ...
1
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0answers
46 views
How do I proceed with the following coulomb integral?
I am trying to solve the $H_{2}^{+}$ ion problem using Fourier transform approach.
The Hamiltonian that I am trying to solve is as follows, $$H=-\frac{\hbar^{2}}{2m_{e}}\nabla^{2}_{e}-\frac{e^{2}}{4\...
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1answer
44 views
How to explain about Raman spectroscopy?
What is the definition of Raman spectroscopy? How to explain in brief about antistoke line and Stoke line and Rayleigh?
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0answers
80 views
What is orthogonalization energy when two atoms overlap?
In this paper, I read that:
When two atoms overlap, quantum mechanics dictates that they be orthogonal to each other. This drives up the energy and leads to so-called Pauli exclusion. The amount of ...
2
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0answers
36 views
Is there a mathematical singularity in the relativistic contraction of valence orbitals as a function of nuclear charge?
I'm looking at Figure 1 on p. 2 of Jansen, "Effects of relativistic motion of electrons on the chemistry of gold and platinum" (2005) (should be a free download). From the bottom curve, there is such ...
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0answers
36 views
Do relativistically-contracted electron states have the same energy and angular momentum values?
I've been reading that electron bound states are defined by four quantum numbers, $n$, $l$, $m_l$, and $m_s$, respectively the principal quantum number, the azimuthal quantum number, the magnetic ...
3
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1answer
111 views
How can I do quantum chemistry with QED?
So I am a theoretical and computational chemist by trade and my usual zone of operation in the domain of quantum mechanics is Hartree-Fock and Density Functional Theories.
I was thinking if there ...
1
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1answer
72 views
How exact are the Kadanoff-Baym equations?
In a General nonequilibrium Quantum chemical System, the Kadanoff-Baym equations have the form:
$(i \partial_t -h_2-\Sigma_{H,2})G_<(1,2) = \delta_C(1, 2) + \int d3 \Sigma (1,3)G_<(3,2)$
where ...
3
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0answers
32 views
Stability of saturated energy levels
In The Feynman Lectures on Physics, Vol. 3, Section 15-5, there's a discussion of the stability of various benzene ions. It turns out that the ions for which the all the energy levels up to a certain ...
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0answers
39 views
Is there a DFT program that gives spin-orbit coupling matrix elements between different spin states of one electron?
I want to calculate spin-orbit coupling matrix element (SOCME) between singlet state and triplet state.
I could get SOCMEs from molpro CASSCF calculation.
Is there any open source DFT package that can ...
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1answer
48 views
Can diffusion occur without thermal motion of molecules?
If I would ask: What are the Basic mechanisms of diffusion? I would get the answer: Because of thermal Brownian Motion.
But are there other causes besides Brownian motion for Diffusion?
Can ...
0
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1answer
24 views
Is the Hartree-Fock approximation getting better and better for higher atoms?
As the atomic number $Z$ increases, is the Hartree-Fock approximation getting better and better, or worse and worse?
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0answers
24 views
Does a Conical Intersection imply that the HOMO-LUMO gap in a molecule is very small?
I came across some notes in which the author swiftly made this comment, that if there's always a large gap between the HOMO and the LUMO along a chemical reaction ("large" can mean at least bigger ...
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0answers
18 views
Why can excited determinants be used as corrections in the MP wavefunction?
So many-body perturbation theory is one way of approximately solving the Schrödinger equation. In Moller-Plesset perturbation theory, the Hamiltonian is expressed as a known part, which is a sum of ...
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0answers
21 views
What is the probability function for a molecule having energy in a certain mode, taking the minimum required quantum energy of that mode into account?
I understand that the probability density for a particular velocity v+dv in one dimension for a molecule in a system is:
$$f(v) = \sqrt{\frac{m}{2\pi k_B T}} \cdot e^{\frac{-mv^2}{k_B T}}$$
I'm ...
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0answers
111 views
many-body problems and why they are so hard
I am currently reading my first course in electronic structure theory and i have questions relating to the complexity of the many-body Schrödinger equation for quantum chemistry. More precisely about ...
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2answers
112 views
How can special relativity account for the electron orbital clouds of (stationary) heavy elements when electrons don't orbit in a classical way?
Einstein's famous mass-energy equivalence equation is still used for calculations, but still often considered less physically meaningful since the atoms that comprise a material don't actually gain ...
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0answers
38 views
Is the following function antisymmetric?
Let there be two hydrogen atoms with its protons at $\vec{R_{1}}$ and $\vec{R_{2}}$ and their electrons are at $\vec X_{1}$ and $\vec X_{2}$ with respect to a global coordinates. Lets also define a ...
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0answers
36 views
Significance of ground state energy in quantum chemistry
I'm reading a paper that says "The fundamental goal in electronic-structure problems is to solve for the ground-state energy of many-body interacting fermionic Hamiltonians" (ref: https://arxiv.org/...
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0answers
16 views
Can electronic energy be independent of nuclear coordinates in the two non interacting hydrogen atom?
I was trying to solve two non interacting hydrogen atoms both nucleus fixed at the the positions $\vec{R_{1}}$ and $\vec {R_{2}}$. I have considered the ground state wave functions of the two ...
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0answers
56 views
Pi-bond angular momentum
I quantum chemistry literatute one can find a statement about projection of the angular momentum on internuclear axis:
The angular momentum vector for rotation about the bond will lie along
the ...
3
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1answer
124 views
Shape of Hydrogen atom in excited state with nonzeros angular momentum
Solution of Schrödinger's equation for an Hydrogen atom is well known:
$$\Psi_{n,l,m} (r, \theta, \phi) = N e^{\frac{-r}{n r_1}} R_n^l (r) P_l^m(cos \theta) e^{im\phi} \,.$$
If we interested with ...
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1answer
74 views
Linear response correlation functions
I'm working my way through Methods of Molecular Quantum Mechanics by R. McWeeny and have run into a derivation I can't seem to figure out.
So in chapter 12, he obtains an expression for the first ...
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1answer
345 views
Why is the distinction between Mott Insulators and Charge Transfer Insulators important?
Strongly-correlated metals often become insulators due to the repulsive Coulomb interaction, and the basic model here is the Mott-Hubbard Model:
$$H=-t\sum(\hat{c}_{i,\sigma}^{\dagger}\hat{c}_{j,\...
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0answers
49 views
What does the spin orbital involed wavefunction mean?
I don't quite understand what do the following expressions mean.
Two spin orbitals multiplication, like $\lvert \alpha \rangle \lvert \beta \rangle$. $\lvert \alpha \rangle$ and $\lvert \beta \rangle$...
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1answer
108 views
What are sigma and pi bonds in physics language?
Chemists often discuss sigma and pi bonds. To a physicist, it's not easy to figure out what these actually are, as discussions tend to be full of lots of chemistry jargon about "antibonding", "...
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1answer
92 views
Corrections from violation of P-symmetry for chemistry, biochemistry, life?
Imagine a mirror image of a biological cell: all molecules replaced with their symmetric versions (enantiomers). At least in theory, we should be able to synthesize it (Wikipedia), for example for ...
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1answer
108 views
Why are high electronegativity atoms found in the periodic table's upper right corner?
Looking at a graphical representation of electronegativity in the periodic table reveals a pattern that, noble gases aside, electrognetivity increases as you move toward the upper right hand corner of ...
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0answers
134 views
Why does my Hartree Fock/SCF code work for small molecules (water, methane etc) but goes crazy for slightly larger ones (Benzene, Butadiene etc)?
I made a Hartree Fock code, in the psi4 package, following the formulas given on this page:
http://sirius.chem.vt.edu/wiki/doku.php?id=crawdad:programming:project3
When I use the same geometry they ...
3
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0answers
327 views
Hartree-Fock decoupling of Hubbard model
Hartree-Fock approximation requires wavefunctions be as separable as possible. I know the basic idea of Hartree-Fock but having some trouble in formalism of second quantization. I am trying to ...
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0answers
28 views
Orbitals and configurations with degenerated energy
When we have to choose, given $n$, $\ell$, where to put an electron, when there are several $m$ orbitals, with the same energy, is there a concrete quantum mechanic rule or some superselection rule to ...
